Applied Computational Economics and Finance by Mario J. Miranda

By Mario J. Miranda

First-class e-book for utilized economics with many examples and usefull Matlab codes. excellent and worthwhile Matlab toolkit.
However, the theoretical part is comparatively susceptible and never coated good.

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Example text

Although this is more complicated, it is accurate regardless of the size of . As gets small, this expression will be approximately 2 /2. Thus, if is about the size of the square root of machine precision (2−26 on most double precision implementations), z would be computed to machine precision with the second expression, but would be computed to be 0 using the first; that is, no significant digits would be correct. Putting all this together, a good approach to computing φ − (y, z) when |y| ≥ |z| uses √  if y < 0 y 1+ 1+ 2+ 2 √ − 2 2 φ (y, z) = 1− 1+ + √ y − if y > 0 2 1+ 2 where = z/y (reverse z and y if |y| < |z|).

An ill-conditioned Jacobian can result in an inaccurately computed Newton step d x, creating severe difficulties for the convergence of Newton and Newton-type methods. In some cases, ill conditioning is a structural feature of the underlying model and cannot be eliminated. However, in many cases, ill conditioning is inadvertently and unnecessarily introduced by the analyst. A common source of avoidable ill conditioning arises when the natural units of measurements for model variables yield values that vary vastly in order of magnitude.

The first is the eigenvalue/eigenvector factorization. Given an n × n matrix A, this factorization finds n ×n matrices Z and D, with D diagonal, that satisfy AZ = Z D. The columns of Z and the diagonal elements of D form eigenvector, eigenvalue pairs. If Z is nonsingular, the result is a factorization of the form A = ZDZ −1 . It is possible, however, that Z is singular (even if A is not); such matrices are called defective. The eigenvalue/eigenvector factorization is unique (up to rearrangement and possible linear combinations of columns of Z associated with repeated eigenvalues).

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